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Unformatted text preview: and a force due to air resistence, which can be accurately modeled as proportional to the velocity v of the object, say-bv for some constant b > . Here, g is the constant acceleration of gravity near the earths surface. By Newtons second law, the force should be equal to the mass of the object times its acceleration dv dt . a) Show that the function v ( t ) = mg b 1-e-bt/m satises m dv dt = mg-bv for all t . b) Calculate lim t v ( t ) . What does it imply about the velocity of the object as time passes? c) For any xed (constant) time t , calculate lim b + v ( b ) . What does it imply about an object falling without air resistence?...
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